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3 years ago

Find the Percent of increase:

Mathematics

1 answer:

BigorU [14]3 years ago

8 0

Answer:

Step-by-step explanation:

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Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x

Dennis_Churaev [7]

Let $f(x)=x^3-3x^2+2x=x(x-1)(x-2)$ . Suppose we define a new function that is $f$ transformed so that it is symmetric about the origin. This can be done with

$g(x)=f(x+1)=(x+1)(x)(x-1)$

Notice that $g$ is an odd function, since

$g(-x)=(-x+1)(-x)(-x-1)=-(x-1)(x)(x+1)$

So if $g(x)$ is symmetric about the origin, this means $f(x)$ must by symmetric about the point $(1,0)$ . This in turn means that the area between $f$ and the x-axis is the same from 0 to 1 as it is from 1 to 2. This means

$\int_0^2f(x)\,\mathrm dx=2\int_0^1f(x)\,\mathrm dx$

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4 years ago

Write 0.0004089 in standard form

Oksi-84 [34.3K]

Answer:

4.08 × 10-4

Step-by-step explanation:

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3 years ago

Jordan is cutting a 2 meter by 1 1/4 meter piece of rectangular paper into two pieces along its diagonal. what is the area of ea

MariettaO [177]

Each piece will have an area which is 1/2 of the area of the rectangle. The diagonal cuts the rectangle in half.

= 1/2 ( 2 * 1/1/4)

= 1 1/4 m^2

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3 years ago

Read 2 more answers

You are in charge of erecting a radio telescope on a newly discovered planet. To minimize interference, you want to place it whe

strojnjashka [21]

Answer:

Step-by-step explanation:

$\text{The equation of the surface of the sphere whose radius is 6 can be represented as:}$

$x^2+y^2+z^2 = 36}$

$So , g(x,y,z) = x^2 + y^2 + z^2 - 36$

$\text{To minimize the function :} \\ \\ M(x,y,z0 = 6x - y^2 +xz + 60$

$\text{by applying lagrange multipliers }$

$\bigtriangledown M (x,y,z) = \lambda \bigtriangledown g(x,y,z)$

$\langle 6+zz,-2y,x \rangle = \lambda \langle 2x,2y,2z \rangle$

$6+z = 2\lambda x$

$-2y = 2 \lambda y$

$\text{from the second equation ;} (\lambda +1)y = 0, \text{so , it is either y =0 or }\lambda = -1$

$Suppose \ \lambda = -1 ; \text{other equation becomes x = -2z and 6+z = -2x}$

$\text{such that; 6+z =4z or z = 2}$

$\text{it implies that: x= -4 and }y = \pm \sqrt{36 - 4-16} = \pm 4$

$\text{Here; there exist two possible points}$

$\text{(-4,-4,2) and (-4,4,2)}$

$\text{In the scenario here y=0,} \lambda \text{ is unknown, then we remove it}$

$x = 2 \lambda z \\ \\ 6+z = 2 \lambda x \\ \\ 6+z = 4 \lambda ^2z \\ \\ 6 = (4 \lambda ^2 -1) z ---(1)$

$z = \dfrac{6}{4 \lambda ^2 -1}$

$x = \dfrac{12 \lambda }{4 \lambda ^2 -1 }$

$\text{recall that; it i possible to divide }4 \lambda ^2 -1 \text{since (1) shows that it cannot be equal to zero.} \\ \\ \text{hence, puttinf this into constraint, whereby y =0, Then:}$